Problem: What is the slope of the line $2y=3x+2$? Express your answer as a common fraction.
Explanation: First, we solve the equation for $y$: \begin{align*}2y&=3x+2 \\ y&=\frac{3x+2}{2} \\ y&=\frac{3}{2}x+1.\end{align*} Now that we have the equation for the line in $y=mx+b$ form, where $m$ is the slope and $b$ is the $y$-intercept, we can see that the slope of the line is $\boxed{\frac{3}{2}}$.